Quasi-convex subsets in Alexandrov spaces with lower curvature bound

doi:10.1007/s11464-021-0955-0

Front. Math. China

2022, Vol. 17

Issue (6) : 1063-1082 https://doi.org/10.1007/s11464-021-0955-0

RESEARCH ARTICLE

Quasi-convex subsets in Alexandrov spaces with lower curvature bound

Xiaole SU¹, Hongwei SUN², Yusheng WANG¹(

)

¹. School of Mathematical Sciences (and Key Laboratory Mathematics and Complex Systems, Ministry of Education, China), Beijing Normal University, Beijing 100875, China
². School of Mathematics Sciences, Capital Normal University, Beijing 100037, China

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Abstract

We introduce quasi-convex subsets in Alexandrov spaces with lower curvature bound, which include not only all closed convex subsets without boundary but also all extremal subsets. Moreover, we explore several essential properties of such kind of subsets including a generalized Liberman theorem. It turns out that the quasi-convex subset is a nice and fundamental concept to illustrate the similarities and differences between Riemannian manifolds and Alexandrov spaces with lower curvature bound.

Keywords Quasi-convex subset Alexandrov space extremal subset quasigeodesic

Corresponding Author(s): Yusheng WANG

Issue Date: 04 January 2023

Cite this article:

Xiaole SU,Hongwei SUN,Yusheng WANG. Quasi-convex subsets in Alexandrov spaces with lower curvature bound[J]. Front. Math. China, 2022, 17(6): 1063-1082.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0955-0
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I6/1063

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